Welcome to my Set Theory Page Set Theory: Foundations of Mathematics The two axioms which define Intuitive Set Theory are discussed below. Ackermann Functions and Transfinite Ordinals An important part of Cantor's set theory, which forms the foundations of mathematics, is the concept of transfinite ordinals. A systematic way of writing the sequence of ordinals is given. Read more Justification of the Continuum Hypothesis Intuitive arguments are given to suggest that Continuum Hypothesis should be accepted. Read more Axiomatic Derivation of the Continuum Hypothesis Continuum Hypothesis is derived from an axiom called Axiom of Monotonicity. Read more Real Set Theory A set theory is defined in which Generalized Continuum Hypothesis and Axiom of Choice are theorems. Read more Intuitive Set Theory A set theory is defined in which Skolem Paradox does not arise. Also, there are no sets which are not Lebesgue measurable. Read more Two Axioms to Extend Zermelo-Fraenkel Theory Axiom of Monotonicity is used along with Zermelo-Fraenkel set theory to derive Generalized Continuum Hypothesis. Axiom of Fusion is used to investigate the cardinality of the set of points in a unit interval. Read more Visualization of Intuitive Set Theory Intuitive Set Theory is defined as the theory we get when axioms of Monotonicity and Fusion are added to ZF theory. Cardinals in the theory are visualized using illustrations. Read more White Hole, Black Whole, and The Book Physical and intellectual spaces are visualized making use of concepts from Intuitive Set Theory. A book containing all the proofs of mathematics is called The Book. Read more The Essence of Intuitive Set Theory The ideas which motivated the defintion of intuitive set theory are explained. Only a passing acquaintance with the transfinite cardinals of Cantor is assumed on the part of the reader. Read more Generalized Continuum Hypothesis and the Method of Fusing The method of fusing explains the basis for the formulation of the axioms of monotonicity and fusion, the two axioms which define intuitive set theory. Read more Generalized Continuum Hypothesis and the Axiom of Combinatorial Sets Axiom of Combinatorial Sets is defined and used to derive generalized continuum hypothesis. Read more Definition of Intuitive Set Theory Two axioms which define intuitive set theory, Axiom of Combinatorial Sets and Axiom of Infinitesimals, are stated. Generalized continuum hypothesis is derived from the first axiom, and the infinitesimal is visualized using the latter axiom. Read more Two Open Problems and a Conjecture in Mathematical Logic The open problems attempt to extend Zermelo-Fraenkel set theory and the conjecture suggests an extension of Godel's incompleteness theorems. Read more Teaching Generalized Continuum Hypothesis Generalized Continuum Hypothesis is derived from a simple axiom called Axiom of Combinatorial Sets. Read more The Mathematical Universe in a Nutshell The mathematical universe discussed here gives models of possible structures our physical universe can have. Read more Derivation of Continuum Hypothesis from Axiom of Combinatorial Sets Continuum Hypothesis is derived from an axiom called Axiom of Combinatorial Sets. The derivation is simple enough to be understood by any novice, who has a passing acquintance with cardinals of Cantor. Read more The advantage with the intuitive set theory is that it allows us to have a simple visualization of our physical and intellectual spaces. K. K. Nambiar ... end of the page ...